The Rational SPDE Approach for Gaussian Random Fields With General Smoothness
Artikel i vetenskaplig tidskrift, 2019

A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form , where is Gaussian white noise, L is a second-order differential operator, and is a parameter that determines the smoothness of u. However, this approach has been limited to the case , which excludes several important models and makes it necessary to keep beta fixed during inference. We propose a new method, the rational SPDE approach, which in spatial dimension is applicable for any , and thus remedies the mentioned limitation. The presented scheme combines a finite element discretization with a rational approximation of the function to approximate u. For the resulting approximation, an explicit rate of convergence to u in mean-square sense is derived. Furthermore, we show that our method has the same computational benefits as in the restricted case . Several numerical experiments and a statistical application are used to illustrate the accuracy of the method, and to show that it facilitates likelihood-based inference for all model parameters including beta. for this article are available online.

Nonstationary Gaussian fields

Matern covariances

Spatial statistics

Stochastic partial differential equations

Fractional operators


David Bolin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Kristin Kirchner

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Journal of Computational and Graphical Statistics

1061-8600 (ISSN) 1537-2715 (eISSN)

Vol. in press



Sannolikhetsteori och statistik




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